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  • If f:[1,infinite)-->[2,infinite) is given by f(x)=x +1/x then f^-1(x) is equal to

If f:[1,infinite)-->[2,infinite) is given by f(x)=x +1/x then f^-1(x) is equal to

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Solution:   We can write    y=fracx^2+1x,

                 or           x^2-yx+1=0

              Rightarrow         f^-1(y)=x=fracypm sqrty^2-42

             Rightarrow          f^-1(x)=fracx+sqrtx^2-42

             Note that   f^-1(x)=fracx-sqrtx^2-42  is not possible because

             f^-1:[2,infty ) ightarrow [1,infty )    and  f^-1(3) otin [1,infty ). 

Posted by

Deependra Verma

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